On the Mathematical Emergence and Physical Constraints of ˙m/m = ˙f /f

This paper examines the derivative identity m˙/m=f˙/f\dot m/m = \dot f/fm˙/m=f˙/f, which formally arises from combining Einstein's mass-energy equivalence E=mc2E = mc^2E=mc2 with Planck's relation E=hfE = hfE=hf. While mathematically valid, the identity is physically ill-typed, as mass and Compton frequency are not generally functions of a continuous parameter. The work provides a rigorous derivation, situates the identity in historical and experimental contexts, and highlights the distinction between formal mathematical results and physically measurable quantities.